# Notation in Serge Lang - Algebra

In Serge Lang's Algebra on page 772 in the middle there is an expression of this form

$$K(A(C))=Z[A(C)]/R(A(C))$$.

I don't understand what $$Z[A(C)]$$ is supposed to mean. Thanks.

• Please provide more context. Not everyone has his book. – Lukas Kofler Sep 11 at 8:58
• You can google a pdf of it. But the C is a K-family and A(C) is a family of objects of C that admit a finite resolution with elements of C. And A is an abelian category. – rrr123 Sep 11 at 9:26

The $$Z$$ denotes the integers, and $$[A(C)]$$ the set of isomorphism classes of objects in $$A(C)$$. Then $$Z[A(C)]$$ is just the free abelian group with generators the elements of $$[A(C)]$$.